AP/Calculus-Based Physics:Kinematics: The Physics of Motion Units

This topic contains a selection of units designed to assist you in teaching motion. Units include frames of reference, graphing skills, motion in one dimension, motion in more than one dimension, vectors, and more. Units are not listed in a prescribed order.

Activities:

This animation takes the fear out of reference frames, and it's fun. All motion is relative to a frame of reference. This resource shows how the motion of a bouncing basketball looks different depending on whether the observer is standing still, walking in the same direction as the player, or walking in the opposite direction. It offers students nine scenarios (frames of reference), and they must answer questions from the observer's viewpoint.

References and Collections:

An "Illumination" is a short chunk of explanatory/exploratory material that addresses a specific topic, usually from a conceptual point of view. These Illuminations contain simulations and were designed primarily for student self-study and practice.

Lesson Plans:

This is a PhET Gold Star winning lesson that helps students build skills in interpreting graphs of motion. It accompanies the PhET simulation "The Moving Man" (see link below) and includes classroom-ready Power Point concept questions, student guide, and assessments.

High school students can often record data and "plug & chug", but have more difficulty in fitting or interpreting data. This exemplary two-week unit on data analysis introduces students to the statistical method known as least squares regression. Using an online tool to plot data, students then calculate regression lines and fit the data to estimated parameters.

Students will apply knowledge of motion by making their own animated sequences that model real-life physical situations. Sound a little zany? Topics include motion in an inertial reference frame, gravity on a falling body, and orbital motion of planets. Fun and creative!

Activities:

With one mouse click, students may create their own customized graphs from among five types: bar, line, area, pie, and X/Y. Various patterns, colors, grids, and label choices allow for customization, with a full tutorial to help in set-up. This resource is cost-free.

This website contains a collection of short videos depicting physical processes commonly discussed in beginning courses. Positions of objects in the video frame can be viewed in step motion or real-time, and then mapped onto video analysis software, allowing for more accurate measurement and graphing.

This set of eleven interactive challenges will help students master motion graphing. Each challenge requires the student to match the motion of an animated car to the correct position/time or velocity/time graph. The activity provides enough repetition to help learners construct a meaningful understanding of why the graphs appear as they do.

Maneuver a simulated man and watch simultaneous graphs of his position, velocity, and acceleration. For beginning learners, the acceleration graph may be closed. Try teaming this simulation with the great companion lessons by PhET teacher-fellows, found under "Lesson Plans" above. Highly versatile resource; adaptable to a broad spectrum of abilities/levels.

Content Support For Teachers:

A very well-organized tutorial on how to construct and interpret three basic kinematic graphs: P/T, V/T and A/T. It includes animated examples, links to five worksheets, and related problems for student exploration.

Student Tutorials:

This is a web-based homework problem that helps students understand velocity vs. time graphs (v vs. t). A sequence of user-activated questions guides beginners through a full conceptual analysis before introducing the math. Based on PER principles (physics education research).

A companion to the resource above, this online tutorial explores the importance of the slope of v-t graphs as a representation of an object's acceleration. Self-guided evaluations help students overcome common misconceptions.

An assessment designed by the award-winning Modeling Instruction team. It assesses a student's ability to create and also interpret motion maps, p-t graphs, and v-t graphs. Could be used either as a class review or as a unit test. Downloadable in pdf format.

This is an exemplary set of Power Point materials for teachers to introduce vector basics, including vector addition/subtraction and how to calculate vector components. See Assessments below for a companion unit test. All may be freely downloaded. To read about the underlying pedagogy employed by the authors, go to Reference Material below and click on Bridging the Vector Calculus Gap.

Activities:

Students explore several kinematics situations involving different starting positions and speed. Velocity and acceleration vectors are displayed in real-time graphs as the action is animated. Requires Java plug-in.

This Java applet gives a visual representation of the addition of vectors. Students can choose to add 2-5 arbitrary vectors. The applet adds the vectors visually, moving each to the sum of the previous vectors.

Any vector directed in two dimensions can be thought of as having two parts (components). This Java applet, developed by a high school teacher, demonstrates how to find the magnitude of these components. The component vectors can be in any directions relative to the given vector or relative to each other.

If students are to perform calculations relating to dynamic torque and magnetic forces, they need a firm understanding of vector cross products. This Java simulation lets them observe the cross product from different vantage points as they spin the plane on which A and B lie.

Want to give your students a chance to explore vector addition without tackling the math? This simple Java simulation lets them draw two vectors by clicking and dragging the cursor. The components, magnitude, and direction will be displayed; then click "Add" to see the vector sum.

Student Tutorials:

This tutorial, part of the respected Physics Classroom web site, is an Editors' Top Choice. It discusses fundamentals and operations of vectors, plus in-depth support in understanding vector addition and resolution. Entertaining animations and images accompany the text.

After students have mastered addition of two vectors, let them practice adding three vectors. They will drag and draw the vectors, then attempt to draw the resultant. If they are incorrect, the accurate resultant is drawn for them.

This page is an interactive environment where subjects are organized in flow charts, allowing easy movement from one topic to a related item. Vector resolution, addition, and product are covered in-depth.

As instructors, we may forget that certain representations (like vector arrows) seem like a foreign language to beginning students. This thoughtfully-crafted tutorial introduces vector diagrams in kid-friendly language and extends the learning to interactive practice problems with answers provided.

This comprehensive worksheet on vectors may be used as a test/quiz for beginning physics students. It was designed to accompany the lecture and lesson materials by the same authors (see above under Lesson Plans). May be freely downloaded and printed for classroom use.

Activities:

A simulation to explore the motion of a model car with constant acceleration. The student sets values for initial position, velocity and acceleration -- the simulation creates the real-time graphs. A pair of timers can be placed anywhere along the path of the car to measure the motion at intervals. Can be adapted for grades 6-7 by using only the velocity and position fields.

A very effective problem-based activity to help students understand the universal law of gravitation. They work cooperatively on a mock space mission: a spacecraft is orbiting Iris, a planet with a smaller radius and lower mass than Earth. Students collaborate to find the gravitational acceleration on the surface of Iris and figure out how a human body will react to gravity on the planet.

How does air resistance affect the motion of a free-falling object? In this model, a blue ball falls under the influence of gravity alone. The red ball is subject to both gravity and air resistance. Adjust the amount of air resistance with a slider, then watch the changes in the motion graphs.

Content Support For Teachers:

This item, part of an online textbook, offers in-depth content support for teachers, plus sets of problems related to speed and velocity. It includes creative ideas for classroom investigations that integrate statistics.

This resource offers support in understanding the concept of acceleration as a rate of change. It includes example problems with solutions, homework problems, and a fun section that provides sample accelerations of selected events. Great content support for middle school teachers or solid tutorial for high school physics.

This page offers a clear explanation of the equations that can be used to describe the motion of an object in a straight line. A comprehensive set of algebraic, statistical, and conceptual problems are included. Provides content support for middle school teachers.....also appropriate for high school physics students.

Student Tutorials:

This is a web-based homework problem that helps students understand velocity vs. time graphs (v vs. t). A sequence of user-activated questions guides beginners through a full conceptual analysis before introducing the math. Based on PER principles (physics education research).

Lesson Plans:

This project-based unit explores 2-dimensional motion equations and applies them to the real world phenomena of projectiles. Students build small-scale catapults to investigate the scenario of delivering supplies to a group of hikers stuck across a deep river gorge. Computer modeling techniques are introduced, with extensive support for both teacher and learner. Individual lessons may be pulled out if time is limited.

Students learn about projectile motion and conservation of momentum as they investigate a mock-murder case involving a handgun. They are given just enough data about the gun ballistics and the crime scene to test hypotheses and solve the murder. This resource is based on the PBL (Problem-Based Learning) instructional method. It includes a Teacher's Guide and a Student Manual.

Activities:

Students can have fun exploring projectile motion as they interactively fire objects of varying mass from a cannon. Users may set initial velocity, angle, and air resistance. This resource would be teamed well with the Physics Classroom student tutorial on projectile motion (below).

This simulation would be a good follow-up to the PhET projectile motion applet (above). This item takes the learner to the next level by calculating maximum height, horizontal distance, magnitude of velocity, and total energy of a projected object. Students will set initial height, speed, angle, and mass before firing their projectile. Appropriate for high school or gifted/talented middle school students.

A great activity for getting students excited about projectile motion.....and easily adaptable for the high school classroom. It is a CSI scenario where a man is shot with a handgun. Using the Problem-Based Learning method, students work cooperatively to solve the case by applying physics. This resource includes a printable student manual. Registered teacher-users can also access an Instructor's Guide free of cost.

19 videotaped experiments are organized sequentially here for introducing fundamentals of motion in introductory physics classes. The instructional method is based on cognitive apprenticeship: students focus on the process of science by observing, finding patterns, modeling, testing, and revising. The author is a highly-respected professor of physics, who has done extensive work in physics education research.

This simulation features an airplane flying at constant horizontal velocity, preparing to drop relief supplies to a small island. As captain of the plain, you must calculate the release point for dropping the package and press the red release button at the right moment. The trajectory of the falling package is traced onscreen. If your calculations were off, it will dump in the ocean. Question for students to ponder: what does inertia have to do with it?

Content Support For Teachers:

This easy-to-follow tutorial helps students comprehend how various components work together to determine trajectory: range, height, time, speed, and angle. It includes explanations of algebra-based equations related to projectile motion.

Student Tutorials:

This seven-part resource is an excellent introduction to the characteristics of projectile motion. Through in-depth explanations and animations, it explores vertical acceleration and explains why there are no horizontal forces acting upon projectiles, a common student misconception. The last two sections are devoted to problem solving. Try teaming it with the PhET Projectile Motion activity above.

A unique and highly-engaging tutorial developed by the authors of Australia's PhysClips. Short film clips, photos, and diagrams are integrated with simple text to spark interest. The first two videos feature the classic "Hammer and Feather Drop", both on the moon and on Earth.....a great springboard to discuss air resistance.

Assessment:

This interactive problem goes well beyond the formulas to help learners separately analyze both the horizontal and vertical components of motion in a ball-throwing scenario......before they attempt any math. Great scaffolding is provided from conceptual reasoning through calculation, with immediate feedback for correct and incorrect responses. It also addresses both Math and Language Arts Common Core standards.

Activities:

This set of activities developed by the Exploratorium offers students an entertaining way to see real-world applications of rotational dynamics and principles of circular motion. They will explore forces at work in "The Ollie" and torque forces required for mid-air maneuvers.

For the teacher planning a unit on amusement park physics, this tutorial can double as a student classroom activity. It offers an overview of the forces acting upon a roller coaster as it travels on a straight, curved, or looped track. Free body diagrams and animations depicting kinetic/potential energy also enhance student understanding of a complex set of interactions. (Includes a self-test.)

This is Part 2 of the mock mission to Planet Iris (see Part 1 under the heading "Motion in One Dimension" above). In this scenario, students work in groups to determine the velocity required to maintain a stable orbit at 140m above the surface of Iris. then calculate the thrust necessary to land the spacecraft smoothly. Includes a printable student manual. Registered teacher-users also have access to a comprehensive instructor's guide.

Students will have fun as they design a flat circular highway exit and figure out what the exit speed limit should be. They will be applying concepts of circular motion, static friction, and kinetic friction. For the AP classroom, the activity can be extended to the design of a banked curve. A complete instructor's guide is available free of cost to registered teacher-users.

11 videotaped experiments are organized sequentially here for teaching circular motion in introductory physics classes. The instructional method is based on cognitive apprenticeship: students focus on the process of science by observing, finding patterns, modeling, testing, and revising. The author is a highly-respected professor of physics, who has done extensive work in physics education research.

Can an amusement park Merry-Go-Round be designed to be dangerous? This simple model lets kids discover for themselves how rotational speed and radial distance interact to create a more thrilling ride. Don't miss the page link to "Physiological impact of G-forces". Setting the speed & radial distance at the highest points will result in g-forces that exceed space shuttle re-entry and high speed fighter jets! We suggest using this simulation to introduce rotational quantities and angular velocity.

This interactive simulation offers a way for students to explore the connection between uniform circular motion and simple harmonic motion. It provides a way to visualize SHM as the projection of uniform circular motion onto one axis, which should promote understanding of the basic equation for objects undergoing simple harmonic motion.

Content Support For Teachers:

One of the most deeply entrenched misconceptions among beginning physics students is that centrifugal motion (away from the center) is a "force" in itself. In this tutorial, part of Physics Classroom, the author explains why the direction of force is viewed from an inertial frame of reference in a classical mechanics course and thus why centrifugal motion is not a force in a Newtonian framework.

Student Tutorials:

This resource guides the beginning student through characteristics of circular motion. It is broken into five sections addressing: the mechanics of circular motion, centripetal force, algebraic and trigonometric problems and solutions, and a full chapter that debunks the centrifugal "force" misconception. Interactive problems feature liberal use of diagrams and force vectors to enhance understanding.

This student tutorial illustrates how circular motion principles can be combined with Newton's Second Law to analyze physical situations. Two algebraic problems and detailed solutions are provided, plus a five-step model for solving circular motion problems.

Activities:

HyperPhysics is an exploration environment for concepts in physics which employs concept maps and other linking strategies to facilitate smooth navigation. In exploring any aspect of physics, basic concept understanding is a must. Connections between concepts a plus.

Explore Kepler's Laws in this simulation that allows students to control the size and path of the orbiting object. Don't miss the "About" link to supporting resources: student manuals, assessment materials, and more.

With this orbit simulator, you can set initial positions, velocities, and masses of 2, 3, or 4 bodies, and then watch them orbit each other. The simulation is especially effective at helping students understand how distance and mass are related to orbit. Scroll down on the page for related lesson plans developed by middle school and high school teachers.

Content Support For Teachers:

This set of materials pertaining to Kepler's laws includes equations and properties of conic sections, scale of the solar system, the energy equation for Keplerian motion, and Newton's "Universal Gravitation". It is part of a larger collection that offers lesson plans, lecture materials, and historical background. No calculus is introduced.

Lesson Plans:

This page contains procedures for setting up 20 demonstrations relating to motion. All demos have been fully tested in the classroom and were selected for inclusion because they are engaging, require minimal set-up, and are highly illustrative of key concepts taught in introductory classical mechanics. Historical anecdotes and commentary add to the depth of this unique resource.

Activities:

19 videotaped experiments are organized sequentially here for introducing fundamentals of motion in introductory physics classes. The instructional method is based on cognitive apprenticeship: students focus on the process of science by observing, finding patterns, modeling, testing, and revising. The author is a highly-respected professor of physics, who has done extensive work in physics education research.

An exceptional resource collection on how to integrate "direct measurement videos". These high-speed short videos feature tools for easy analysis of various physical situations: rulers, grids, frame-counters, and screen overlays for making precise measurements. Includes 9 teaching modules with lesson plans, assessments and answer keys, and pedagogical background. Does not require purchase or installation of video analysis software.

References and Collections:

This website contains a collection of short videos (20-40 frames each) depicting physical processes commonly discussed in beginning courses. Positions of objects in the video frame can be viewed in step motion or real-time, and then mapped onto video analysis software, allowing for more accurate measurement and graphing.

This collection of short videos explores the basic physics of football in a way that's sure to spark interest among kids. Each video features an NFL player, file footage of games, slow-motion video captured with a super high-speed Phantom Cam. Physicists appear in each video to explain the concepts and clarify the connection to physics. Topics: Newton's Laws, momentum, inertia, vectors, center of mass, projectile motion, and more.

Activities:

This versatile simulation lets students explore the effects of braking on an object moving with constant velocity. Set the initial velocity, start the applet, and hit the brakes. Graphs of velocity vs. time and position vs. time are simultaneously displayed. You can also set the rate of braking acceleration. This resource will help students build concepts relating to frictional force.

Assessment:

An assessment designed by the award-winning Modeling Instruction team. It assesses a student's ability to create and also interpret motion maps. p-t graphs, and v-t graphs. Could be used either as a class review or as a unit test. Downloadable in pdf.

This comprehensive worksheet may be used as a test-quiz for introductory physics or as a diagnostic assessment for more advanced courses. It was designed to accompany the lecture and lesson materials by the same authors (see above under Vectors: Lesson Plans). May be freely downloaded and printed for classroom use.

This comprehensive self-assessment offers much more than a set of problems. For each of the 37 questions, links are provided to additional explanations. This resource is ideal for self-assessment or as guided practice for learners who are struggling.

Activities:

This simulation is a powerful way to investigate the meaning of shape/slope for 3 types of motion graphs: p-t, v-t, and a-t. Students "match" the motion of a ball whose movement is automatically generated. To do it correctly requires analysis of the motion. Next, learners predict what the graphs will look like by using sliders to generate their own straight-line graphs.

In this model, a ball is launched by a spring-gun in a building with a very high ceiling. The task: calculate an initial velocity so that the ball barely touches the 80-foot ceiling. Students can test their answers by setting the initial velocity on the simulation, then watch the ball's path. Graphs of position vs. time or velocity vs. time can be turned on to view the ball's motion as a function of time.

We like the simplicity of this model for introducing free fall and gravitational acceleration. Students can control the initial height, set initial velocity from -20 to 20 m/s and change the gravitational constant. The free fall is displayed as a motion diagram, while graphs are simultaneously displayed showing position, velocity, and acceleration vs. time.

Student modeling provides a great opportunity for kids to test and apply their own prototypes to explain and predict physical phenomena. This model includes explicit step-by-step directions for building the computer model with Easy Java Simulations, a program that greatly reduces the amount of programming required. It asks students to develop a computer model for a ball moving vertically under the influence of gravity. Editor's Note: The activity requires that students have first collected data of a basketball or volleyball bouncing under a motion detector.